ABOUT A NONLOCAL BOUNDARY-VALUE PROBLEM FOR ELLIPTIC DIFFERENTIAL EQUATIONS WITH SAMARSKII–IONKIN CONDITIONS OF INTEGRAL TYPE

In this paper, we study one abstract nonlocal boundary-value problem with Samarskii–Ionkin conditions of integral type for the differential equation of elliptic type (Formula presented.) in an arbitrary Banach space E, where the operator A is positive. We establish well-posedness of this problem in various Banach spaces. We prove theorems on the well-posedness of several nonlocal boundary-value problems for elliptic equations with Samarskii–Ionkin conditions of integral type as an application. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.